Question

Vectors! Please help! This is the last question OF MY WHOLE SEMESTER! I've tried it so many times and can't get it right. :(

Answer 1

Pictures always help; see the one I've attached for reference.

Call the first vector (from HQ to the supply drop) u and the second vector (from supply drop to medics) v. We then want to find w, the vector from the medics to HQ, which corresponds to the vector -(u + v). (This is because u + v is the vector pointing from HQ to the medics; we're talking about the one in the opposite direction.)

Write the vectors in horizontal/vertical component form:

u = (125 km) (cos 235º x + sin 235º y) = (-71.70 x - 102.39 y) km

v = (75 km) (cos 110º x + sin 110º y) = (-25.65 x + 70.48 y) km

Why these angles?

• "55 degrees south of west" is 235º; due west is 180º from the positive horizontal axis, and you add 55º to this
• "20 degrees west of north" is 110º; due north is 90º, so add 20º to this

Add the vectors:

u + v = (-97.35 x - 31.92 y) km

Multiply by -1 to get the vector w:

w = -(u + v) = (97.35 x + 31.92 y) km

The distance covered by this vector is equal to its magnitude:

||w|| = √((97.35 km)^2 + (31.92 km)^2) = 102.45 km

The direction θ is given by

tanθ = (31.92 km)/(97.35 km)  ==>  θ = 18.15º